Born in the town of Metsovo (Epirus, Greece, then Ottoman Empire) Averoff moved to Alexandria while still young. He was known through most of his life for founding numerous schools in both Egypt and Greece.

As a benefactor, he contributed funds for the restoration of the Panathenian Stadium in readiness for the 1896 Summer Olympics. This he did at the request of Crown Prince Constantine. The stadium was refurbished in 1895, its second refurbishment in the 19th century, using white marble from Mount Penteli pursuant to Averoff's request. The cost was initially estimated at 585,000 drachmas but eventually reached 920,000.

He also served as a member of the reception committee for the foreign competitors at the Games.
In gratitude for his contributions, a statue of Averoff was commissioned and placed in front of the Panathenian Stadium. It remains there today.

In addition, a Greek cruiser, the flagship of the Hellenic Navy, which was constructed largely with funds (2,500,000 Gold francs) provided for under his will, was named after him.